- "Numbers rule the Universe"
- Samos Pythagoras
Nice letter Mr.Robert,
Well as far as the world knows there exists no such accurate formula for the nth prime. But the fascination is that, primes being the builder blocks of all the integers remain mysteriously an unfound concept so far.
Well, to introduce myself first, I am Sudarshan Iyengar from India (hope you all have heard about my country), India is the place where 0 originated. From time immemorial people of India have worked a lot in order to find the pattern of primes. The basic difficulty is due to the adoption of the base 10 system which hides the pattern of the occurrence of primes. Primes when seen geometrically speaks to us better than when it is viewed as a number under base 10 system.
We all are familiar with the Fundamental Theorem of Arithmetic which states that:-
"Every positive integer(greater than 1) can be expressed as the product of primes in one and only one way, except for the order in which primes are multiplied".
This tells us the beauty of the arrangement of all integers. As bricks are for buildings so are primes for integers. Every number takes the support of prime number(s) for its formation. That is why it is termed as "PRIME" which means "Of Utmost Importance".
It is also said in Hindu mythology that primes are equivalent to god. If one can understand primes then it means that he has understood god, that is why it is pretty difficult for one to analyse the behaviour of primes.
Among the positive integers, 1 is being treated as god, and the prime numbers are being termed as fairies, and every object in the universe is compared to that of composite numbers. Fairies(Primes) stand with the support of god(1) and themselves. Where as all other objects of the universe(composites) stand with the support of god(1) and one or more number of fairies(primes).
If one wants to study the distribution of primes, one needs to look into it naturally.
It is well said by Srinivasa Ramanujan that:
"An equation means nothing to me unless it expresses a thought of God. "
As we can observe, every great mathematician is supposed to be known as a great philosopher as well. Not much can be done by a mathematician if he doesn't relate his work with that of philosophical thinking.
Here goes a well known quote which says:
"Nature speaks to us in the language of mathematics".
So, the duty of a mathematician is not just to think of mere logic about the truth of the statements, he should make an attempt to see the beauty of nature through mathematics.
Phil Carmody is doing a great job by taking care of this discussion group. I hope that we being the members of this group should make an attempt to crack this so called "Mystery of Prime numbers" by a good deal of investment of our team work.
Hoping to receive your mails from all of you,
Mr. Robert wrote the following:
----- Original Message -----
Sent: Tuesday, April 30, 2002 6:12 AM
Subject: [PrimeNumbers] Re: research on the nth prime?
This closest approximation of the Nth prime that is based soundly on
theory would be the result yielded by "The Prime Number Theorem"
which states that pi(x) = x/[ln(x)-1]. Here, pi(x) is the average
number of primes less than x; hence, if pi(x)=10000, then the prime
lying closest to x is approximately the 10000th prime number.
I agree with Richard, however; while the primes appear to be randomly
distributed, I too wonder if there is still not a "structure" to
their distribution waiting to be discovered.
--- In primenumbers@y..., Richard Traynham <therichardt@y...> wrote:
> --- Jud McCranie <jud.mccranie@m...> wrote:
> > At 05:34 PM 4/29/2002 +0000, padmapani19 wrote:
> > >i am wondering if there's a formula for generating
> > the nth prime
> > >however ineffecient it might be.
> > There are ways to compute the number of primes < x
> > without having to > generate all of the primes < x.
> Ah the search for the "magic generating function"...
> As I recall there is a quadratic equation that
> generates the first 20 or so primes with no extras
> or missing ones. But, then it fails.
> I find it difficult to believe (might just be
> my ignorance here) that there's an equation that
> is accurate to the tick for calculating the number
> of primes below a certain value. It seems to
> me that the primes almost must be distributed
> randomly (or something like that). Of course,
> I have always wondered if there is some sort of
> "structure" to the distribution of primes and
> prime twins in particular. hmmm
> (Been way to busy at work to do anything with
> primes for some time now :(
> "People have spent more time thinking about prime
> numbers than have ever spent thinking about war."
> (not an exact quote) -- Constance Reid.
> TheRichardT@Y... (Do you Yahoo?)
> Check out my web site: http://www.mac-2001.com
> (A haven for the discussion of "Meaningful Ideas")
> "If you take a dog and feed him and make him famous,
> he will not bite you. That is the principle
> difference between a dog and a man" -- Mark Twain.
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